Tension (Angles and Inclines)

1. The problem statement, all variables and given/known data
A 15kg block sitting on a 22(degree) incline is held stationary by a string as shown. The coefficient of friction between the block and the surface of the incline is 0.12.

Well, I notice that both Tension Force and Force Friction are along the same path, therefore I believe those are the two variables?

Well, yes. But not for your reasoning. The reason is that the force of static friction is variable. μsFn only represents the maximum force that static friction can apply, but it is possible for static friction to apply less or even no force at all.

You're asked to find the minimum tension in the rope. When do you think the force of tension will be minimum?
When the static friction is zero? When the static friction is maximum? Or somewhere in between?

Well, yes. But not for your reasoning. The reason is that the force of static friction is variable. μsFn only represents the maximum force that static friction can apply, but it is possible for static friction to apply less or even no force at all.

You're asked to find the minimum tension in the rope. When do you think the force of tension will be minimum?
When the static friction is zero? When the static friction is maximum? Or somewhere in between?

I noticed you mentioned static friction.

Since the object is at rest, I believe that the static friction is somewhere in between.

Since the object is at rest, I believe that the static friction is somewhere in between.

It can be somewhere in between. Or it can be maximum. Or it can be zero. All of these are valid possibilities. But for each of these options, the force of tension will be different.
When will the force of tension be minimum? Are you saying tension is minimum when the force of friction is somewhere in between it's minimum (zero) and it's maximum?

It can be somewhere in between. Or it can be maximum. Or it can be zero. All of these are valid possibilities. But for each of these options, the force of tension will be different.
When will the force of tension be minimum? Are you saying tension is minimum when the force of friction is somewhere in between it's minimum (zero) and it's maximum?

147cos68 = 64.70102431 N
^ This is my adjacent, a.k.a. my Gravitational Force parallel. Should the opposite of it not equal to both the Tension Force and Frictional Force combined? I thought that is how equilibrium works.

I am having difficulty finding the correct formula to solve. My assumptions are that (0.12 Mew * Normal Force) is my maximum Frictional Force? The issue is also found when I try to find the adjacent for the 22 degree triangle.